Question

You begin saving for retirement at age 25, and you plan to retire at age 60. You want to deposit a certain amount each month into an account that pays an APR of 3% compounded monthly. Make a table that shows the amount you must deposit each month in terms of the nest egg you desire to have when you retire. (Round your answers to the nearest cent.)

Nest egg size	Needed deposit
$100,000	$
$200,000	$
$300,000	$
$400,000	$
$500,000	$
$600,000	$
$700,000	$
$800,000	$
$900,000	$
$1,000,000	$

Answer 1

The formula for the future value (F) of an annuity is F = P [(1+r)ⁿ-1]/r or, P = F*r/[(1+r)ⁿ-1]/ where P is the periodic payment, r is the interest rate per period and n is the number of periods. Here, r = 3/1200 = 1/400 = 0.0025 and n = (60-25)*12 = 35*12 = 420. Therefore, [(1+r)ⁿ-1]/r = [(1.0025)⁴²⁰-1]/0.0025 = (2.853909143-1)/0.0025 = 1.853909143/0.0025 so that [(1+r)ⁿ-1]/r= 0.0025/1.853909143

1. If F = 100000, then P = (100000)* 0.0025/1.853909143 = $ 134.85
2. If F = 200000, then P = 2*134.85 = $ 269.70
3. If F = 300000, then P = 3*134.85 = $ 404.55
4. If F = 400000, then P = 4*134.85 = $ 539.40
5. If F = 500000, then P = 5*134.85 = $ =674.25
6. If F = 600000, then P = 6*134.85 = $ 809.10
7. If F = 700000, then P = 7*134.85 = $ 943.95
8. If F = 800000, then P = 8*134.85 = $ 1078.80
9. If F = 900000, then P = 9*134.85 = $ 1213.65
10. If F = 1000000, then P =10*134.85 = $ 1348.50

The table is as under:

Nest egg size ($)	Needed deposit ($)
$100,000	134.85
$200,000	269.70
$300,000	404.55
$400,000	539.40
$500,000	674.25
$600,000	809.10
$700,000	943.95
$800,000	1078.80
$900,000	1213.65
$1,000,00	1348.50